Detection of C′,Cα correlations in proteins using a newtime- and sensitivity-optimal experiment

Article

Detection of C¢,C

correlations in proteins using a new

time- and sensitivity-optimal experiment

Donghan Lee

*, Beat Vo¨geli

& Konstantin Pervushin

*

Laboratory of Physical Chemistry, ETH Ho¨nggerberg, HCI, CH-8093, Zu¨rich, Switzerland;

b

NCI-Frederick, NIH Frederick, 21702, MD, USA

Received 17 August 2004; Accepted 22 November 2004

Key words: 13-carbon observation, chemical shift correlation, residual dipolar coupling, scalar coupling, sensitivity enhancement

Abstract

Sensitivity- and time-optimal experiment, called COCAINE (CO-CA In- and aNtiphase spectra with sensitivity Enhancement), is proposed to correlate chemical shifts of 13C¢ and 13Ca spins in proteins. A comparison of the sensitivity and duration of the experiment with the corresponding theoretical unitary bounds shows that the COCAINE experiment achieves maximum possible transfer efficiency in the shortest possible time, and in this sense the sequence is optimal. Compared to the standard HSQC, the COCAINE experiment delivers a 2.7-fold gain in sensitivity. This newly proposed experiment can be used for assignment of backbone resonances in large deuterated proteins effectively bridging13C¢ and 13Ca reso-nances in adjacent amino acids. Due to the spin-state selection employed, the COCAINE experiment can also be used for efficient measurements of one-bond couplings (e.g. scalar and residual dipolar couplings) in any two-spin system (e.g. the N/H in the backbone of protein).

Introduction

Recently developed transverse relaxation-optimized spectroscopy (TROSY) (Pervushin et al., 1997) has opened a new avenue for investi-gating large macromolecule using NMR spectros-copy, since the sensitivity of spectra is dramatically increased due to the reduction of transverse relaxation (Pervushin et al., 1998). Further reduction can be obtained by uniform or partial replacement of non-labile protons with deuterons (Grzesiek et al., 1993; LeMaster, 1994; Yamazaki et al., 1994; Shan et al., 1996; Gardner and Kay, 1998; Salzmann et al., 1998). The sequential backbone resonance assignment of large proteins has been achieved with the usage of TROSY-type

triple-resonance experiments (Mulder et al., 2000; Salzmann et al., 1999a, b ; Yang and Kay, 1999) together with the deuteration of non-labile pro-tons. Among these experiments, TROSY-type HNCOCA and HNCACO experiments are used for matching intra-residual cross-peaks of the HNCA experiment with the strong sequential cross peaks derived from the HNCO experiment. However, their application has been limited to low field spectrometers by rapid13C¢ transverse relax-ation, due to the large 13C¢ chemical shift anisot-ropy (CSA).

A recently proposed 3D MQ-HACACO exper-iment (Pervushin and Eletsky, 2003) gives similar information to the TROSY-type HNCOCA and HNCACO experiments. Moreover, the experiment is very favourable in terms of relaxation, since the period involving transverse magnetization is

*To whom correspondence should be addressed. E-mails: dhlee@ncifcrf.gov; kope@phys.chem.ethz.ch.

minimized by a double- constant-time evolution period (Swapna et al., 1997), in which the1HaA13Ca multiple quantum coherences (Grzesiek et al., 1995a, b ; Swapna et al., 1997; Xia et al., 2000) are used simultaneously to record 1Ha and 13Ca chemical shifts and to achieve the 1Ha magneti-zation transfer to the 13C¢ spins for acquisition (Serber et al., 2000, 2001). In addition, the acqui-sition on13C keeps the pulse sequence shorter than the HNCOCA and HNCACO experiments by omitting several polarization transfer periods for the magnetization transfer from13C¢ to1H, which result in a significant signal loss (Braun et al., 2003). However, the 3D MQ-HACACO experi-ment requires at least partial reprotonation at Ha positions, which can cause sensitivity loss due to the relaxation originating from the Ha(Grzesiek et al., 1993; Pervushin et al., 1997).

Here we propose a sensitivity enhanced, time-optimal experiment called COCAINE (CO-CA In- and aNtiphase spectra with sensitivity Enhancement) experiment to correlate chemical shifts of 13C¢ and 13Ca spins, which is applicable to the sequential backbone assignments of fully or partially deuterated proteins. In the framework of this new experiment both Boltzmann reservoirs of thermal equilibrium magnetizations of 13C¢ and 13Ca spins are constructively utilized (Per-vushin et al., 1998). A comparison of the sensi-tivity and duration of the experiment with the corresponding theoretical unitary boundaries im-posed by quantum spin dynamics shows that in the absence of relaxation maximum possible polarization transfer is achieved in the shortest possible transfer time. The performance of the experiment is compared with the standard HSQC approach and is shown to deliver sensitivity gains of factor 2.7 without an increase in the duration of the experiment. The COCAINE experiment can also be used for efficient measurements of

13

C¢ and13Caone bond couplings (e.g. scalar and residual dipolar couplings), due to the spin state selection employed (Andersson et al., 1998; Cor-dier et al., 1999; Lerche et al., 1999; Sørensen et al., 1999). The proposed principle underlying the COCAINE experiment can also be extended to time-optimal detection of H/N and H/C correla-tions with water suppression by a WATERGATE sequence (Piotto et al., 1992) before the acquisition and by presaturation, respectively.

Results and discussion

Unitary bounds and time-optimality of polarization transfer for the spin-state selection in the

COCAINE experiment

The efficiency of polarization transfer experiments can be assessed by comparison with fundamental bounds imposed by unitary spin dynamics using available quantum control Hamiltonians (Glaser et al., 1998; Khaneja et al., 2003a, b ). The unitary bound value, bmax, defines the largest projection of

an arbitrary source operator A on a target opera-tor C achievable by a unitary propagaopera-tor U (Glaser et al., 1998),

bmax¼ maxðTrfU A UyCg=TrfCyCgÞ ð1Þ

The unitary bound value can be determined numerically for arbitrary initial and target opera-tors (Glaser et al., 1998). This number represents an important benchmark for construction and evaluation of NMR experiments utilizing non-selective rf-irradiation and heteronuclear J cou-pling described by Hrf and HJ Hamiltonians,

respectively. The second parameter, which should be considered for an optimal experiment, is the minimal time, Hmin, needed to transfer

magneti-zation between these states (Untidt et al., 1998; Untidt et al., 1999; Khaneja et al., 2001, 2003a, b ; Schulte-Herbruggen et al., 2001; Reiss et al., 2002; Skinner et al., 2003).The polarization transfer (between the time points b and c in Figure 1) for the spin-state selection in the COCAINE experi-ment using the magnetization originating from spin I consists of two independent pathways that are schematically represented by:

p

2IzS
! bðUCOCAINEÞð
1=2ÞI
ðE þ 2SzÞ

¼ bðUCOCAINE_{Þð
1=2ÞI
S}a_{; ð2:1Þ}

p

2IzSþ! bðUCOCAINEÞ1=2I
ðE
2SzÞ

¼ bðUOCAINE_Þ1=2I
Sb_{; ð2:2Þ}

where the normalized operatorsp2IzS
,

p 2IzSþ,

1/2I)Sa and 1/2I)Sb are used. Analysis shows that for both pathways of Equations (2) bðUCOCAINE_{Þ ¼ b}

max¼

p

2 indicating that in the absence of relaxation the maximum possible sensitivity for this type of polarization transfer is

actually achieved in the experiment. The magnetiza-tion originating from spin S can be described by changing Izto Ixor Iyin the Equations (2.1) and (2.2).

The COCAINE experiment accomplishes the polarization transfer in s=1/(2JIS) seconds,

corre-sponding to the shortest possible time. Indeed, the transfer of Equation (2.1) consists of two pathways 2IzSx !
2IxSz and 2IzSy!
Iy. The first

path-way can be implemented using just rf-Hamiltonians in a negligibly short amount of time. The second pathway represents the so called anti-phase transfer between hermitian operators with the maximal theoretical efficiency of btheorðtÞ ¼ sinðpJIStÞ for the

transfer time t 1=ð2JISÞ and 1 for t > 1=ð2JISÞ (the

formal proof along the lines of Theorem 3 of Reiss et al. (Reiss et al., 2002) is presented in Supporting materials). Thus, the minimal time required to pro-duce the transfer of Equation (2.1) is tmin¼ 1=ð2JISÞ,

which is indeed achieved experimentally. The same bound for minimal transfer time is applicable for the pathway of Equation (2.2) as well as for the pathways starting on spin S. Thus, the COCAINE experiment attains both theoretical benchmarks (maximum

transfer and minimal time) and by those measures is optimal.

In- and anti-phase [13C,13Ca]-correlation experiment

Figure 1 shows the pulse scheme of the COCAINE experiment, utilizing both Boltzmann steady-state magnetizations of I and S spins. For simplicity, we consider first the evolution of the density operator originating from the I spin. For the downfield component of S spin doublet, the first and second phase cycling steps are required. The steady-state magnetization of the spin I is transferred to the spin S and the density operator rI at the time point a in Figure 1 (the first step in the phase cycle in Figure 1) may be described by:

rIðaÞ ¼ IzSþþ IzS
: ð3Þ

After the frequency-labeling period of spin S (time point b in Figure 1), the density operator is given by:

Figure 1. Pulse scheme of the COCAINE experiment. The rows marked I, S, and K represent the rf-channels. Narrow and wide bars stand for 90 and 180  pulses, respectively. All phases are set to {x,} unless indicated otherwise. For the13_Ca-^13

C¢ correlation spectra, the13C¢,13

Caand2H spins were represented by I, S, and K, respectively. The13C¢,13

Caand2H carrier frequencies are set to 174, 55 and 3.2 ppm, respectively.2H decoupling is performed with the WALTZ pulse sequence at cB1=2.5 kHz. The delay s corresponds to

1/(41_J

IS) (4.7 ms for

13

Ca-^13C¢ correlation). The line marked PFG (pulsed field gradient) indicates the magnetic field gradients applied along the z-axis: G1, amplitude = 19 G/cm, duration = 0.5 ms; G2, 50 G/cm, 0.9 ms. The spectra of upfield and downfield

components of doublets are obtained in the interleaved manner using the following phases: for the downfield U1={y,)x,)y,x,},

U2={y,x,)y,)x,} w1={)y,)y,)y,)y,} w2 (receiver) = {y,)x,)y,x}; and for the upfield U1={y,)x,)y,x}, U2={y,x,)y,)x},

w1={y,y,y,y}, w2(receiver) = {y,)x,)y,x}, respectively. The phase-sensitivity in the t1dimension is obtained by recording a second

FID for each t1value using for the downfield U1={)y,)x,y,x}, U2={y,)x,)y,x}, w1={y,y,y,y}, w2(receiver) = {)y,x,y,)x}; for the

upfield U1={)y,)x,y,x}, U2={y,)x,)y,x}, w1={)y,)y,)y,)y}, w2(receiver) = {)y,x,y,)x}, respectively. The data is processed by the

rIðbÞ ¼
expð
ixst1ÞIzSþ
expðixst1ÞIzS
:

ð4Þ The subsequent polarization transfer step (points b to c) transforms the operators IzSþand IzS
to the

operators I)Sa and I)Sb, respectively, resulting in the density operator at the time point c:

rIðcÞ ¼
1=2i expð
ixst1ÞI
Sa

þ 1=2i expðixst1ÞI
Sb: ð5Þ

The downfield component of the doublet is achieved by changing the sign of I)Sb(the second step in the phase cycle in Figure 1).

The evolution of the density operator rS origi-nating from the steady-state magnetization of the spin S is similar to the evolution of rI. At the time points a, b and c the density operators are given by: rSðaÞ ¼
iIxSþþ iIxS
; ð6:1Þ

rS_{ðbÞ ¼
expð
ix}

st1ÞIxSþþ expðixst1ÞIxS
;

ð6:2Þ

rSðcÞ ¼
1=2i expð
ixst1ÞI
Sa

1=2i expðixst1ÞI
Sb: ð6:3Þ

In analogy with the evolution of rI, the downfield component of the doublet is achieved by changing the sign of I)Sb(the second step in the phase cycle in Figure 1).

The COCAINE type-correlation spectra con-tain individual components of doublets in the di-rectly acquired dimension with two-fold gain in sensitivity due to the utilization of both Boltzman steady-state magnetizations, compared to the HSQC spectrum. A further 2 gain in sensitivity is achieved by the fact that all terms present during t1

evolution period lead to observable magnetization during the acquisition. Thus, the total theoretical gain of COCAINE amounts to 2 2 of the inten-sity of the corresponding S-coupled HSQC.

The validity of the COCAINE approach is shown for a sample of uniformly 2H, 13C, 15 N-labeled ubiquitin in 95%1

H2O/5%2H2O at pH 7.3

and 20C. Figure 2 compares a region of the HSQC spectrum with the COCAINE experiment recorded using the pulse scheme of Figure 1. The suppression of the second doublet component was better than 93% in all cases. The unsuppressed

Figure 2. Contour plots of (a) the 13Ca-coupled [13C¢, 13

Ca]-HSQC without the decoupling during t2 and (b) the COCAINE

experiment acquired with a uniformly2H,13C,15N-labeled ubiquitin in 95%1H2O/5% 2

H2O at pH 7.3 and 20C, using a DUX probe,

which is optimized for the13_{C detection, in a Bruker Avance spectrometer operating at the}1_{H frequency of 600 MHz. In order to}

record both spectra (the13_Ca_{-coupled [}13

C¢,13_Ca_{]-HSQC and the COCAINE), t}

1max=19.8 ms, t2max=100 ms and 90 (cB1=2.5 kHz)

and 180 (cB1=3.3 kHz) selective pulses with Gaussian lineshape truncated at 5% were used. The overall suppression of second

doublet component is better than 93%. The resulting spectrum of the COCAINE experiment shows the downfield component of each doublet. Comparison of two spectra illustrates the simplification achieved by the COCAINE spectrum due to the elimination of13Ca splitting. The solid lines mark 1D slices (I) and (II), used for the sensitivity comparison in Figure 3.

second doublet component may be due to the13C pulse imperfection on the selectivity, variable relaxation of the multiquantum coherence in the

13

Capathway, the13Ca–13Cbcouplings, and/or the difference in the longitudinal relaxation of 13Ca and13C¢spins (Pervushin and Eletsky, 2003) (Fig-ure 2). Thus, accurate values of homonuclear one-bond couplings can be obtained from the difference in the 13C¢ frequencies for pairs of doublet components. The observed sensitivity gains of between 2.4 and 2.8 differ slightly from the theoretical calculation (Figure 3). These variations may be due to variable relaxation of the multi-quantum coherence in the 13Ca pathway, the

13

Ca–13Cb couplings, and/or the difference in the longitudinal relaxation of13Ca and13C¢spins (Per-vushin and Eletsky, 2003). Nontheless, the average sensitivity gain of 2.7 in the COCAINE experiment, compared to the HSQC experiment, is in excellent agreement with the theoretical value of 2 2.

Since the COCAINE experiment utilizes spin-state selection, it can also be used for efficient measurements of one-bond couplings (e.g. scalar and residual dipolar couplings) in any two-spin system (e.g. the N/H in the backbone of protein). However, the water suppression (i.e. a WATER-GATE sequence (Piotto et al., 1992) before the acquisition is necessary for proton detection. It is

worth noting that the suppression of the second doublet component was better than 97% in [15N,1H]-COCAINE experiment and the sensitiv-ity gain, compared with the method suggested by Lerche et al. (Lerche et al., 1999), depends on the relative size of 15N steady-state magnetization to

1

H steady-state magnetization.

Conclusions

We have demonstrated that the sensitivity is sig-nificantly increased by the COCAINE experiment, compared to the corresponding HSQC and that in fact it achieves the theoretical maximum transfer. Furthermore, the COCAINE experiment simpli-fies the spectra in 13C-observed NMR spectros-copy by eliminating the13Casplitting without any special processing (Serber et al., 2001; Pervushin and Eletsky, 2003). The COCAINE experiment can also be processed to isolate the two doublet components, allowing for its use in measurement of one-bond couplings (scalar and residual dipolar couplings) to obtain structural constraints. Using the newly proposed experiment, the backbone assignment of large proteins can be achieved by connecting information from the most sensi-tive triple-resonance experiments (TROSY-type HNCA and HNCO).

Supporting materials

Maximum anti-phase transfer between hermitian operators, available in electronic format at http://dx.doi.org/10.1007/s10858-005-2361-4.

Acknowledgements

We thank Dr. Fred Damberger for careful reading of the manuscript. Financial support was obtained from a Swiss National Science Foundation grant to K.P.

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